1. Field of the Invention
The present invention relates to a method and apparatus for making a magnetic field analysis on a magnetic circuit including a permanent magnet of which the properties are subject to change due to demagnetization. The present invention also relates to a method for producing a permanent magnet by using such a method and apparatus for magnetic field analysis.
2. Description of the Related Art
Recently, to design a magnetic circuit more efficiently and to further reduce its size, magnetic field analysis has sometimes been carried out using a computer simulation technique. Such magnetic field analysis may be performed by a method such as a finite element method in which permanent magnets with various shapes are evaluated by dividing them into a huge number of very small elements (or meshes). As those magnetic field analysis techniques have been developed, it has become possible to calculate the magnetic flux density distribution or flux in a magnetic circuit with high precision. For example, a conventional magnetic field analysis method is described in the following prior art document:                Document: Yasuhito Taniguchi and four others, “Three-Dimensional Magnetic Field Analysis on Permanent Magnet Motor with Skew Considered”, [online], [searched through, and found on, the Internet on Oct. 2, 2002], <URL: http://www.jri.co.jp/pro-eng/jmag/analysis/papers/skew.pdf>.        
When a rare-earth permanent magnet is heated, its magnetization decreases (which is called a “demagnetization phenomenon”). Meanwhile, a ferrite magnet produces the demagnetization phenomenon when cooled. Those demagnetization phenomena include a “reversible demagnetization phenomenon” in which a magnet recovers its original magnetization when brought back to a normal temperature and an “irreversible demagnetization phenomenon” in which a magnet cannot recover its original magnetization even when brought back to the normal temperature. The magnitude of the reversible demagnetization changes linearly with the temperature of the magnet and its rate is called a “reversible temperature coefficient”. On the other hand, the irreversible demagnetization refers to the decrease in magnetization that has been caused by heating or cooling but cannot be compensated for even when the magnet temperature is brought back to room temperature again.
For example, suppose a permanent magnet is used at 100° C. In that case, even if the temperature of the magnet is decreased to a normal temperature (20° C.) after the irreversible demagnetization has been produced, the magnetization of the magnet remains low and cannot recover its original level fully. Once such demagnetization has occurred, the hysteresis curve of the magnet changes its shape.
In carrying out a magnetic field analysis on a magnetic circuit including a permanent magnet, the magnetic field analysis needs to be performed with the demagnetization of the permanent magnet taken into consideration. However, a conventional demagnetization estimating method just determines whether or not demagnetization occurs in a permanent magnet under given operating conditions (such as temperature and external magnetic field). Hereinafter, this point will be described with reference to FIGS. 1 through 3.
FIG. 1 illustrates a plate-shaped permanent magnet. The permanent magnet illustrated in FIG. 1 is magnetized in its thickness direction. FIG. 2 is a cross-sectional view schematically illustrating the magnetic lines of force produced by that permanent magnet. As can be seen from FIG. 2, the magnetic paths of magnetic lines of force emitted from the vicinity of the ends of the magnet are shorter than those of magnetic lines of force emitted from the center portion of the magnet.
Once a permanent magnet has been magnetized, the permanent magnet produces an N pole and an S pole. Accordingly, as shown in FIG. 2, a magnetic flux (i.e., magnetic lines of force) is produced so as to head from the N pole toward the S pole outside of the permanent magnet. In this case, another magnetic flux heading from the N pole toward the S pole has been produced inside of the permanent magnet, too. The magnetic flux produced inside of the magnet acts in such a direction as to decrease the magnetization of the permanent magnet. This is why a magnetic field formed by such a magnetic flux is called a “demagnetizing field (self demagnetizing force)”. The closer the N and S poles are, the greater the demagnetizing force. In the plate-shaped permanent magnet shown in FIG. 1, the larger the ratio of the plate thickness to the plate area, the greater the demagnetizing force.
FIG. 3 is a graph schematically showing a portion of the demagnetization curve of the permanent magnet shown in FIG. 1. As used herein, the “demagnetization curve” refers to either the second or third quadrant portion of a hysteresis curve, which is obtained by starting to change the magnetic field monotonically in a state where a permanent magnet has a saturated magnetic flux density or saturated magnetic polarization. FIG. 3 is a graph of which the ordinate represents the magnetic flux density B and the abscissa represents the external magnetic field H and shows only the second quadrant portion. In the graph shown in FIG. 3, a demagnetization curve is drawn as an approximated line. However, even if at least a portion of the hysteresis curve of a magnet is linear, that hysteresis curve will also be referred to herein as a “B-H curve”.
In the graph shown in FIG. 3, a point corresponding to the demagnetizing force Hd (i.e., the operating point) is designated on the B-H curve. The magnetic flux density at this operating point is equal to Bm and the line connecting the operating point to the origin of the graph is called an “operating line”. And the absolute value of the slope of the operating line is called a “permeance coefficient Pc”. The magnetic flux density Bm is one of numerical values that depend on the permeance coefficient Pc.
The demagnetizing force Hd is always present no matter whether or not an external field is applied to a permanent magnet. Accordingly, the density of the magnetic flux emitted from a permanent magnet to which no external field is applied is equal to the magnetic flux density Bm corresponding to the operating point. It is generally said that the operating point of a permanent magnet changes with the shape of the magnet or its surrounding conditions. Strictly speaking, the operating point is also changeable from one position to another in the permanent magnet. That is to say, the permeance coefficient Pc of a permanent magnet is not constant in that permanent magnet but changes from one position to another in the permanent magnet.
As shown in FIG. 2, the shorter the magnetic path, the smaller the demagnetizing force Hd and the larger the permeance coefficient Pc. Stated otherwise, the longer the magnetic path, the greater the demagnetizing force Hd and the smaller the permeance coefficient Pc. For that reason, in the permanent magnet having the shape shown in FIG. 1, the permeance coefficient Pc becomes the smallest at the center of the magnet and the largest at the corners of the magnet. In FIG. 1, Pc(min) denotes a site with the minimum permeance coefficient Pc and Pc(max) denotes a site with the maximum permeance coefficient Pc.
In this manner, the permeance coefficient Pc of a permanent magnet changes according to a specific position in the permanent magnet. On the other hand, the demagnetization produces where the permeance coefficient Pc is the smallest. Thus, in the conventional magnetic field analysis method, the magnetic flux density values Bm at respective sites of a magnet (i.e., a number of finite elements) are obtained and then the permeance coefficient Pc(min) at a site with the smallest magnetic flux density Bm is calculated by a computer simulation technique. Thereafter, by comparing an operating line having such a permeance coefficient Pc(min) with a B-H curve at an operating temperature, it is determined whether or not this site can be demagnetized. Hereinafter, such a conventional demagnetization estimating method will be described with reference to FIG. 4.
FIG. 4 is a graph showing a B-H curve of a permanent magnet at a normal temperature (20° C.) as a solid curve and another B-H curve thereof at 100° C. as a dotted curve. The B-H curve data at respective temperatures are stored in a memory of a computer. After data about the shape of a permanent magnet has been fed, the operating lines are obtained for respective sites in the magnet by a finite element method.
The graph of FIG. 4 also shows two operating lines of two types of magnets C and D. The operating line C is supposed to be the operating line of a site that has the smallest permeance coefficient Pc in the magnet C, while the operating line D is supposed to be the operating line of a site that has the smallest permeance coefficient Pc in the magnet D. Also, these two magnets C and D are supposed to share the same B-H curve for the sake of simplicity.
As can be seen from FIG. 4, the intersection between the operating line C and the 20° C. B-H curve and the intersection between the operating line C and the 100° C. B-H curve are both located above the inflection points (i.e., knick points) of their associated B-H curves. Thus, it is expected that the magnet C with the greater permeance coefficient Pc(min) would not be demagnetized even under an operating environment at 100° C.
On the other hand, although the intersection between the operating line of the magnet D with the smaller permeance coefficient Pc(min) and the 20° C. B-H curve is located above the inflection point (i.e., knick point) of its associated B-H curve, the intersection between the operating line of the magnet D and the 100° C. B-H curve is located below the inflection point (i.e., knick point) of its associated B-H curve. Thus, it is judged that the magnet D with the smaller permeance coefficient Pc(min) would not be demagnetized at 20° C. but would be demagnetized at 100° C.
Such a conventional magnetic field analysis method just determines whether or not a site that has the smallest permeance coefficient in a permanent magnet is demagnetized. Accordingly, even if that portion with the smallest permeance coefficient accounted for such a small percentage of the overall permanent magnet that the demagnetization problem hardly occurs in practice, the decision could still be “demagnetization should occur”.
Also, the conventional magnetic field analysis method could not give any answer to the question of what the magnetic flux density distribution would be like after the demagnetization occurred. That is to say, the conventional magnetic field analysis method just tested each magnet for the probability of occurrence of demagnetization and was unable to show, by numerical analysis, how the flux and magnetic flux density distribution would change as a result of the demagnetization.
In order to overcome the problems described above, a primary object of the present invention is to provide a method and apparatus for magnetic field analysis, contributing to not only determining whether or not demagnetization would occur in a permanent magnet but also calculating its magnetic flux density distribution after the demagnetization.